We collect several variants of the proof of the third case of the Bessaga-Klee relative classification of closed convex bodies in topological vector spaces. We were motivated by the fact that we have not found anywhere in the literature a complete correct proof. In particular, we point out an error in the proof given in the book of C. Bessaga and A. Pełczyński (1975). We further provide a simplified version of T. Dobrowolski's proof of the smooth classification of smooth convex bodies in Banach spaces which also works in the topological case.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-5,
author = {Marek C\'uth and Ond\v rej F. K. Kalenda},
title = {Note on Bessaga-Klee classification},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {59-74},
zbl = {1326.52001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-5}
}
Marek Cúth; Ondřej F. K. Kalenda. Note on Bessaga-Klee classification. Colloquium Mathematicae, Tome 139 (2015) pp. 59-74. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-5/